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3 years ago

Select all expression that are equivalent to 64 2/3.

Mathematics

1 answer:

pav-90 [236]3 years ago

8 0

Answer:

<h2>Option B and D</h2>

Step-by-step explanation:

As,

${64}^{ \frac{2}{3} } = {(\sqrt[3]{64})}^{2} = \sqrt[3]{ {64}^{2} }$

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Find the volume of the wedge with vertices at points (0,0,0), (1,0,0), (0,1,0), (0,0,1) by integrating the area of cross-section

Angelina_Jolie [31]

Answer:

V = 1/6 cubic units

Step-by-step explanation:

Applying the concept of integrals for volume calculation:

$V = \int\limits^b_a {S(x)} \, dx$ (1)

V = volume of the solid bounded by x = a and x = b

S(x) = cross section area of the solid, perpendicular to the x axis

From the figure we have that S is the area of a triangle that has base Z and height Y

Area of the triangle = $S(x)=\frac{y(x)*z(x)}{2}$ (2)

Calculation of y(x) and z(x)

We apply the equation of the point-slope line (plane xy):

Slope = $m = \frac{y_{2} - y_{1} }{x_{2} - x_{1}}$ (3)

Equation of the line = $y - y_{1} =m(x-x_{1} )$ (4)

Replacing the points (1,0) and (0,1) in (3):

$m=\frac{1-0}{0-1} =-1$

Replacing the point (1,0) and m = -1 in (4):

$y-0=(-1)(x-1)$

y(x) = -x + 1 (Line A-B) (5)

We apply the equation of the point-slope line (plane xz):

Slope = $m = \frac{z_{2} - z_{1} }{x_{2} - x_{1}}$ (6)

Equation of the line = $z - z_{1} =m(x-x_{1} )$ (7)

Replacing the points (1,0) and (0,1) in (6):

$m=\frac{1-0}{0-1} =-1$

Replacing the point (1,0) and m = -1 in (7):

$z-0=(-1)(x-1)$

z(x) = -x + 1 (Line A-C) (8)

Replacing (5) and (8) in (2)

$S(x) = \frac{(-x + 1) * (-x + 1)}{2} =\frac{(-x + 1)^{2} }{2}$ (9)

Replacing (9) in (1) and knowing that a = 0 and b = 1:

$V = \int\limits^1_0 {\frac{(-x + 1)^{2} }{2}} \, dx = \int\limits^1_0 {\frac{x^{2}-2x+1 }{2}} \, dx$

$V =\frac{1}{2} (\frac{x^{3} }{3} -2\frac{x^{2} }{2} +x)$ evaluated from x=0 to x=1

$V= \frac{1}{2} (\frac{1}{3} -1 +1) = \frac{1}{6}$

3 0

3 years ago

A sock drawer contains 5 different colors of socks. It has 20 white, 10 black, 10 gray, 6 red, and 4 purple. If you reach into t

suter [353]

20+10+10+6+4=50 socks in total, therefore 10/50 =1/5

6 0

3 years ago

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Which of the following numbers is divisible by 9? A.) 111 B.) 222 C.) 333 D.) 444

Leto [7]

Answer:

Step-by-step explanation:

3+3+3=

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3 years ago

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6x + 8=5x + 12 i don’t get this

NeX [460]

Answer: x = 4

Step-by-step explanation:

6x + 8 = 5x + 12

-8 -8

6x = 5x + 4

-5x -5x

x = 4

5 0

2 years ago

The piper family arrived at the campground at the time shown on the clock. I took the family 2 hours and 15 minutes to get to th

aleksklad [387]

Answer:

As you included no picture, I do not know the time on the clock. We can however, work with assumed figures which you can then relate to your question.

Assuming the time on the clock was 10:45 am, if the family took 2 hours and 15 minutes to get to the camp ground, simply subtract this from 10:45 to find out what time they arrived.

Subtract the 2 hours from 10am:

= 10 - 2

= 8am

Subtract the 15 minutes from 45:

= 45 - 15

= 30

Put that together:

= 8:30 am

They left their house at 8:30 am using this scenario. 

8 0

3 years ago